1. Introduction

The extensive assortment of modern technology is facilitated through the intense interaction between electromagnetic fields and matter. As we advance into the deep subwavelength regime the light-matter interaction or more broadly the electromagnetic field confinement demonstrates astounding properties, which are promising in the fields of sensing [1], nonlinear optics [2], surface photocatalysis [3], etc. Evanescent waves being one of the exquisite deep subwavelength phenomena can strongly confine the electromagnetic field within the deep-subwavelength (much smaller than the operating wavelength) spatial dimensions. The evanescent waves are non-propagating, exponentially decaying electromagnetic fields restricted to the proximity of the interface [4]. There are numerous examples of such evanescent waves, ranging from optical surface waves such as surface plasmon polaritons to total internal reflection that are applied in the fields of total internal reflection fluoroscopy [5], subwavelength imaging [6], attenuated total internal reflection spectroscopy [7], chemical and biosensing [8,9], etc. In this respect, strong resonant evanescent orders can be supported by metagrating. The metagratings are composed of periodically arranged subwavelength rectangular ridges that have been investigated theoretically and experimentally and also applied in context to sensing [10], holograms [11] and various other fields [12]. Grating, as a conventional optical device can diffract the incident wave into several diffraction orders, which can lead to the excitation of evanescent orders too. The number of these diffraction orders is defined by the wavelength of incident light, grating period and is governed by the Fraunhofer’s grating Eq. (1) [13],

 

Fig. 1. (a) Schematic representation of diffraction phenomenon of grating when operated at the subwavelength regime, where higher order modes are restricted in the proximity of the grating surface. (b) The optical surface profilometry scan of the fabricated sample. (c) Schematic illustration of custom-made THz-TDS setup. (d) Schematic representation of NSTM setup.

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In this context, the field of THz technology have experienced a significant expansion, over the past decades. The terahertz radiations occupy electromagnetic spectrum between microwave and infrared radiation which consist of electromagnetic waves typically between 0.1 THz to 10 THz [15]. As the THz spectrum appears between photonic and electronic domains, optical or electronic or a blend of both can be employed towards the generation, processing and detection of THz waves. Many common materials such as biomolecules [16], proteins [17], organic molecules [18], living tissues [19] etc possess THz fingerprints that permit them to be analysed, identified and imaged [20]. Also, THz radiations are safe for screening applications because of its non-ionizing characteristics [21]. In addition to the disciplines that form its base, the THz research finds applications in practical areas namely pharmaceutical quality control [22,23], weapon detection [24], high-speed communications [25–27], materials characterization [28,29] etc, bearing the evidence of its multidisciplinary nature. However, THz technology is still relatively underdeveloped in comparison to photonics and microwave technologies due to the lack of natural materials responsive in this spectrum range. In this context, subwavelength structures (meta structures) such as metamaterials [30–32], metagratings [33], etc. have shown tremendous potentials in advancing THz technology by permitting waveguiding [34], switching [35–38], beam steering [39], modulation [40,41], etc. Many useful THz devices, such as absorber [42], polarization converters [43], etc. have also been derived using subwavelength artificial structures or meta structures. However, exploration of deep sub-wavelength phenomena can contribute to the development of THz devices. Therefore, in this work, we have studied deep subwavelength evanescent orders excited in terahertz metagratings. Additionally, in order to excite pronounced evanescent orders, we have delved different metagrating designs. Typically, the efficiency of the evanescent orders excited in subwavelength metagratings is majorly dependant on periodicity of the grating, polarization of incident wave and effective refractive indices of grating medium or fill factors [44]. However other parameters such as height of the grating can also influence the evanescent order excitations. Therefore, we have designed and investigated one dimensional dielectric metagratings to exploit the evanescent orders for orthogonal polarizations of incident THz radiation and the influence of grating height (at fixed fill factor) on the excited evanescent orders. For that purpose, we have investigated (experimentally and numerically) the evanescent orders with the help of near field THz microscopy assisted by the Fourier transformation [45]. This unique combination can allow physical insights in the studies of resonant evanescent orders at THz domain occurring at length scales much smaller than the operating wavelength (∼ λ/20), basically deep subwavelength dimensions. Additionally, our demonstrated gratings are fully dielectric avoiding metal components, therefore devoid of any plasmonic losses, hence can sustain stronger evanescent orders in the THz frequencies.

2. Sample preparation and characterization

The proposed design of the metagrating is composed of intrinsic silicon substrate having 460 µm thickness (t) on which silicon ridges of 10 µm height (h) and 50 µm width (w) are arranged with a periodic distance (d) of 100 µm. The illustrative representation of the grating design is shown in the inset of Fig. 1(a). The fabrication of metagrating is carried out by using standard UV-photolithography technique ensued by deep reactive ion etching. A clean silicon wafer (> 5000 Ω cm) is coated with photoresist on which the photolithography is performed using a pre-designed photomask to obtain the desired grating pattern. The reactive ion etching is employed to etch away the silicon, producing ridge-groove pattern in silicon wafer (Fig. 1(a) & 1b). The surface profile of the fabricated sample is inspected by utilizing an optical profilometer and is illustrated in Fig. 1(b). The presence of minor distortion along the long edges of silicon ridges is due to the fabrication limitations, precisely due to the etching process.

The transmission response of the fabricated grating is obtained by availing the terahertz time domain spectroscopy (THz-TDS). The custom-made THz-TDS setup comprises of femtosecond laser (Femto synergy laser, 800 nm, 80 MHz, 10 fs) and four parabolic mirrors. The schematic representation of the THz-TDS setup is illustrated in Fig. 1(c). The femtosecond laser is split into two parts with the help of a beam splitter for generation and detection of THz using the <110 > oriented ZnTe crystal (using standard electro-optical technique) and photoconductive antenna based on LT-GaAs (BATOP, GmbH) respectively [46]. The THz pulse (generated by one part of the femtosecond laser beam) is transmitted through the sample and is collected at the receiver. Using the pump probe principle (another part of the split laser beam), the transmission response of the sample is obtained in time domain at the receiver side. Further, Fast Fourier Transform (FFT) on these measurements deliver the transmission as a function of frequency [29]. Here, the transmitted THz through grating sample is normalized using the THz pulse through air. To prevent unwanted THz wave absorption by water molecules present in ambience, the complete characterization system is purged with dry nitrogen gas [47].

Furthermore, the near field response of the grating sample is investigated by employing the Near-field Scanning Terahertz Microscopy (NSTM). The THz-NSTM is a unique instrument that consists of parabolic mirrors, beam splitter that divides the pump and probe beams, a reflector to delay the pump beam and a X-Y-Z motorised stage that supports the sample for 2D spectral and temporal nearfield imaging (Fig. 1(d)). A photoconductive antenna (BATOP GmbH) is used to generate the source THz field, whereas to detect the output field, a polarization sensitive photoconductive antenna based nearfield tip (Protemics GmbH) [48] is used (Fig. 1(d)). The generated field is collimated and focused on the sample with the help of parabolic mirrors. The nearfield tip then experiences a transient current due to the transmitting THz electric field, which is amplified (SR570) and detected using the standard lock-in technique (SR830).

3. Results and discussions

The THz transmission characteristics are measured for two incidence configurations; one where the polarization of incident electric field is parallel to the grating lines (TE, along y-axis in Fig. 1) whereas in another case, the magnetic field is parallel to the grating lines and the electric field is perpendicular to grating lines (TM, along x-axis in Fig. 1). The experimentally measured THz transmission responses of the grating sample are presented in Fig. 2(a) and 2(b) for TE and TM configurations respectively. It can be observed that Fabry-Perot resonances are dominant in the transmission spectra for both the incidence polarizations. The free spectral range of the designed metagrating is calculated to be 99 GHz (approximately). Followed by the THz transmission characterizations, we inspected the grating with the help of CST Microwave Studio for detailed insights. CST is a commercially available 3D numerical simulation software package that solves the Maxwell’s equations by employing suitable boundary conditions and meshing options like tetrahedral, hexahedral etc. To simulate the grating structure as an infinite array of periodically imitated identical elements, numerical simulations are performed in transmission mode with normal incidence using open boundary conditions in the propagation direction and unit cell boundary conditions in the x and y spatial directions (see, Fig. 1), where z-axis is the direction of wave propagation. The transmission response acquired through numerical simulations are emphasized in Fig. 2(c) and 2(d) for TE and TM incidences respectively. It is evident that the simulated results are generally in agreement with the experimental data depicting the Fabry-Perot oscillations in transmission spectra. The black dashed line represents the subwavelength boundary for the designed metagrating which can be derived using grating Eq. (1). The transmission within the subwavelength regime (to the left of the black line) is dominated by the Fabry-Perot oscillations, indicating the Fabry-Perot resonance cavity like behaviour of grating with multiple internal reflections. Gratings operating in this region are also known as metagratings. Whereas, beyond the subwavelength operating range (right side of the black line depicting the boundary), the transmission response is a mix of Fabry-Perot oscillations along with guided resonant modes [49].

 

Fig. 2. (a) and (b) demonstrates the THz transmission of the fabricated Si-air metagrating obtained experimentally for TE and TM configurations respectively. The numerically obtained THz response of the metagrating are shown in (c) and (d) for TE and TM responses respectively. The black dashed line represents the subwavelength boundary for the designed metagrating.

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Moreover, intending to understand the diffraction profiles of the fabricated metagratings, we have measured the electric field intensities at various distances from the grating interface (along z) using NSTM over the frequency range of 0.2 THz to 0.9 THz. The photoconductive near-field tip is scanned along the grating vector (along x) with 2 µm step to capture the spatial electric field distributions after transmitted through the grating. Here, NSTM measures the electric fields as a function of time at each point, which is later converted to frequency domain by applying FFT [45]. From the collected data at several distances (along z), a precise set of electric field values are obtained for each z value (e.g., 10 µm, 20 µm, 50 µm). Further, employing Fourier transformation on these captured electric fields delivers an insight into the propagating and non-propagating modes over a broad frequency range (0.2 THz – 0.9 THz) by providing the diffraction profile of the grating in k-space (momentum space). The diffracted orders in this context might be either negative or positive integer values (m = ±1, ± 2, ± 3, …), with m equal to 0 being the zeroth order (the propagating mode in this case). The experimentally obtained diffraction profile of the grating operating at 0.2 THz to 0.9 THz frequency domain for TE and TM configuration is elucidated in Fig. 3. Here, the blue dotted line highlights the subwavelength boundary in momentum space (k-space). The diffraction modes lying inside blue lines are the propagating modes having moduli of 2π/λ, whereas the higher order modes lying outside the subwavelength regime are evanescent in nature [13]. It is evident from Fig. 3, that the central bright peak (m = 0) propagates energy into the far-field regime, whereas the modes outside the subwavelength regime (m = -1, m = 1) do not propagate energy into the far-field and decays exponentially indicating the evanescent nature [50]. To support the experimental findings, the diffraction profile of the metagrating is also investigated through numerical simulations at the Fabry-Perot peak where the electric field is captured for various distances away from the grating interface. Similar to the experimental analysis, we have employed FFT to the captured electric field values to obtain the diffraction profile and the obtained results are provided in the Supplement 1 (S1). As a consequence of stronger field confinement in case of TM incidence, the simulated field amplitudes of TM modes belonging to higher order modes are stronger than the TE incidence (see, Visualization 1 and Visualization 2 for TE and TM configuration respectively). The simulation and experimental results are well corroborating with each other, see S1 in Supplement 1. It is notable that the evanescent orders (m = ±1) appear close to ±9800m^-1. The subsequent study is carried out at the Fabry- Perot peak near the subwavelength boundary (0.88 THz) within the subwavelength regime (basically, meta regime), but one can also make similar studies at other Fabry-Perot peaks inside the subwavelength regime for similar effects since the diffracted orders are dominated by the Fabry-Perot effects. However, the diffracted orders captured at lower frequencies are relatively weaker due to the reduced photon energy, which is apparent in the diffraction profiles obtained by numerically derived results (Fig. S1).

 

Fig. 3. The diffraction profiles of the experimentally obtained results over the frequency range of 0.2 THz to 0.9 THz after employing FFT. (a – c) Embodies the diffraction profile in case of TE incidence for difference distances (10 µm, 20 µm, 50 µm) away from the grating surface (along Z) whereas (d – f) represents the diffraction profile for TM incidence.

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Additionally, in order to verify the evanescent nature of the higher diffraction orders, we mapped the peak electric field values of higher orders as a function of distance away from the grating interface for both the incident polarizations and are depicted in Fig. 4(a) and 4(b). We used exponential decay fitting to represent the exponential decay characteristic of higher orders using the observed data. Also, the numerical verification of the evanescent characteristics of the higher orders is carried out and is illustrated in Fig. 4(c) and 4(d) for TE and TM configurations respectively. The decay lengths of the evanescent orders that are captured experimentally in the TE and TM configurations are 18.21 µm and 12.61 µm respectively, whereas numerically obtained evanescent orders show decay lengths as 15.26 µm and 12.41 µm for TE and TM configurations respectively. Both experimentally and numerically obtained results confirm the exponential decay characteristics of higher order modes at deep sub-wavelength spatial dimensions (< λ/20). It should be noted that due to fabrication constraints, the configuration of the silicon ridges may deviate from the intended design. (Figure 1(b)), leading to some discrepancy between the simulation and experiment results. Considering the successful excitation and detection of deep subwavelength evanescent orders through 1-dimensional metagratings, we have further extended the work through extensive numerical simulations. Therefore, we have explored the effect of grating heights on excitation of evanescent orders by maintaining the total device thickness constant as 460 µm (h + t) similar to our experimental studies. The height dependant peak amplitude of evanescent fields of the +1 order of the designed metagrating is emphasized in Fig. 4(e) and 4(f) for TE and TM incidences respectively. It can be observed that the strength of evanescent order is dependent on the height of the subwavelength grating and also on the polarization of the incident probe field.

 

Fig. 4. (a) and (b) depicts the exponential decay characteristics of +1 evanescent order which is obtained through experimental measurements for TE and TM cases respectively. Similarly, (c) and (d) represent exponential decay characteristics of numerically obtained evanescent grating orders. The error bars represent the deviations in the experimental values which might be occurring due to fabrication deformities. The exponential decay as function of grating height is emphasized in Fig. (e) and (f) for TE and TM configuration respectively.

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We further focus on the effects of grating height on evanescent order strengths for +1 evanescent order. The field values of +1 order at 10 µm distance from the grating-air interface considering several grating heights ranging from 0 µm (without grating) to 100 µm are extracted through numerical simulations for both the TE and TM configurations. Figure 5(a) and 5(b) represent the obtained simulated field strengths of evanescent order as a function of grating height. It is observed that, the evanescent field amplitudes for gratings with extremely small heights (in this case for less than 5 µm) show insignificant excitation of evanescent orders due to lack of field confinements inside the thin grating groove. The evanescent orders achieve maximum amplitude at height of ∼ 40 µm and ∼ 60 µm for TE and TM configurations respectively. To understand the origin of this observation, we have captured the induced electric field strengths at different grating heights. For TE case the electric field is captured for 5 µm, 40 µm and 80 µm height while for TM case the grating electric field is captured for 10 µm, 60 µm and 100 µm height, basically surrounding the ridge heights corresponding to peak electric field amplitude. The captured electric field profiles are represented in Fig. 5, where Fig. 5(b)–5(d) show the electric fields in TE configuration whereas Fig. 5(f)–5 h the electric fields in TM configurations for different grating heights. The electric field confinement is steep in the case of 40 µm and 60 µm grating heights for TE and TM configurations when compared to other grating heights, because of which the metagratings attain strongest excitation of evanescent orders with maximum amplitude. Our observations demonstrate that if the grating height matches well with the Fabry-Perot resonant cavity then the evanescent orders achieve maximum amplitude. Also, as a consequence of form birefringence and effective refractive indices, the evanescent orders attain their maximum amplitude at different heights for the TE and TM configurations [51]. With further increase in grating height the field confinement inside the grating decreases resulting in decrease in amplitude of evanescent orders which finally saturates (Fig. 5(a) & 5(b)).

 

Fig. 5. Numerically captured amplitude of +1 evanescent grating order at distance of 10 µm away from the grating-air interface as a function of grating height is illustrated in (a) and (b) for TE and TM configurations respectively. (c)-(e) illustrates the electric field profile of the metagrating with different grating height for TE case whereas (f)-(g) depicts the electric field profile of the metagrating for TM case.

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4. Conclusions

In this work, we have explored deep sub-wavelength (< λ/20) characteristics (precisely, resonant evanescent orders) in one-dimensional metagratings operating at THz frequencies for orthogonal probe polarizations (TE and TM). Position-dependent transmitted electric field intensities are recorded using NSTM for broad THz frequencies spanning 0.2 THz to 0.9 THz. Fast Fourier transform on the position dependent fields provides distinct information of diffraction orders efficiently decoupling propagating and non-propagating (evanescent) modes. We have observed decay of evanescent orders at the length scale less than λ/20, that means, within deep subwavelength regime. Further, with the aim of optimizing grating geometry in order to excite prominent evanescent orders, an extensive study over the influence of grating height on the induced evanescent orders is carried out numerically. Our obtained results show that the evanescent orders attain maximum amplitude around 40 µm (∼ λ/9) and 60 µm (∼ λ/6) grating heights for TE and TM incidences respectively. We attribute such thickness dependent excitation to the presence of form birefringence; this means the effective refractive index of grating towards the excitation of evanescent orders for orthogonal incident polarizations (TE and TM) are different. Thus, controlling the grating geometry along with the polarization of probe electric field can accomplish an optimized excitation of evanescent orders at length scales much smaller than the operating wavelength. Therefore, the current study can be promising for developing compact functional devices for THz photonics by exploiting strong field confinements at ultra-small length scales.